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  • 1
    Electronic Resource
    Electronic Resource
    The four sets of additive quantum numbers of SU(3) (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2756-2762 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The four maximal sets of additive quantum numbers and related fine gradings of the Lie algebra sl(3,C) are described in detail. The quantum numbers are determined by a grading of the Lie algebra, fine gradings providing maximal sets of them. Two sets of additive quantum numbers are equivalent precisely if the corresponding gradings are equivalent under a transformation from the automorphism group of the Lie algebra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528509
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    New gradings of sl(3,C) representations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 2763-2769 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two new gradings of the Lie algebra sl(3,C) are the refined sl(2,C) and o(3) gradings. The grading in each case utilizes the sl(2,C), or o(3), weight together with a new additive modular label. A complete set of sl(3,C) representation basis states labeled by each to the two sets of additive quantum numbers is found. The newlabeling operator in both cases fails to commute with the cubic sl(3,C) Casimir operator, and hence mixes states of the contragredient representations (p,q) and (q,p)
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528510
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    The Pauli matrices in n dimensions and finest gradings of simple Lie algebras of type An−1 (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 665-673 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Properties of the Lie algebra gl(n,C) are described for a basis which is a generalization of the 2×2 Pauli matrices. The 3×3 case is described in detail. The remarkable properties of that basis are the grading of the Lie algebra it offers (each grading subspace is one dimensional) and the matrix group it generates [it is a finite group with the center of SL(n,C) as its commutator group].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528006
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Clebsch–Gordan coefficients for SU(5) unification models (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 258-271 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Clebsch–Gordan coefficients for the product (1001)⊗(1001), where (1001) is the adjoint representation of SU(5), with respect to the group basis and the subgroup basis in the reduction SU(5)&supuline;SU(3)×SU(2)×U(1) are computed. One of the basic tools in this computation is the exhaustive use of the Verma algorithm to find bases for the weight subspaces of dimension higher than 1. It allows for the construction of bases in a systematic way by using the so-called Verma inequalities. Only the coefficients for the dominant weights are calculated. The other ones can be obtained by using the elements of finite order (charge conjugation operators) of SU(5).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527655
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Graded contractions of sl(3,C) (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2310-2318 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Wigner–Inönü contraction is generalized to include gradings other than Z2 and the formalism is applied to obtain all toroidal contractions of sl(3,C). Examples of contractions based on nontoroidal gradings are also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529154
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  • 6
    Electronic Resource
    Electronic Resource
    Orbit–orbit branching rules between simple low-rank algebras and equal-rank subalgebras (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1618-1626 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complete orbit–orbit branching rules, or equivalently, reduction of Weyl group orbits, between each simple algebra of rank 3 or less, and its equal-rank subalgebras and between F4 and each of its equal-rank subalgebras are given. The generic case An&supuline;An−1×U(1), the subjoining F4(approximately-greater-than)B3×U(1), and E8&supuline;E6×A2 (first and seventh highest weight labels nonzero) are also treated. Branching rules between rank 4 and 5 simple algebras and E6 and their equal-rank subalgebras are available in a depository.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529687
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  • 7
    Electronic Resource
    Electronic Resource
    Polynomial icosahedral invariants (1988)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 29 (1988), S. 1736-1745 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper the ring of polynomial invariants of the icosahedral group I is studied. It begins by reviewing the surprising connections that this group and its double cover II have with various areas of mathematics and physics of current interest. Information concerning the representation theory of these groups is then given. After a brief discussion of the methods involved, the integrity basis of the ring of polynomial invariants for each irreducible representation of I is given, together with syzygies. These are expressed in terms of the invariants of the tetrahedral subgroup T of I. Finally other methods of finding these invariants are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.527871
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    SL(3,C) generator matrix elements in a Pauli subgroup basis (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 4860-4880 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We construct SL(3,C) basis states reduced according to its finite subgroup ℘3. Matrix elements of sl(3,C) generators are calculated between ℘3 basis states. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533383
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  • 9
    Electronic Resource
    Electronic Resource
    Graded contractions and kinematical groups of space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 405-425 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: G-graded contractions of the complex Lie algebra B2 and of its real forms are considered. It is found that a particular G=Z2×Z2 is a proper choice of the grading group preserved when graded contractions leading to Lie algebras of the kinematical groups of space–time are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530893
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  • 10
    Electronic Resource
    Electronic Resource
    A construction of transitively differential groups of degree 3 (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 443-458 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Some general results on Lie algebras of first order differential operators in n real variables with polynomial (degree ≤3) coefficients are demonstrated. An infinite family of specific Lie algebras and the corresponding Lie groups are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530792
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